Smooth the join between 2 separate meshes
I don't exactly understand what you are trying to achieve by separating the limbs from the body but IMHO there is no way to get rid of the line. 

If you have two separate objects or even two sub-meshes that aren't connected, you will always have a visible line where they seem to be connected. This is just how shading in every renderer (at least the ones I know) works. And that's the reason why almost every 3D artist will keep limbs connected to the body. 

Besides that your 3D Viewport is set "Solid" shading. In this mode your scene gets a basic material with basic lightning setup. That setup will make the line even more prominent compared to "Render View" with an actual light setup and a material applied. It might help a little, but you will never get rid of the line entirely.